IAPWS-IF97 Verification

What is calculated

PhaseGauge uses the IAPWS Industrial Formulation 1997 for the thermodynamic properties of ordinary water substance. The calculation engine is pinned to iapws-if97@2.8.0. Calculations use MPa, K, kJ/kg, and kJ/(kg·K); display-unit conversions do not alter the stored results.

Viscosity, thermal conductivity, surface tension, static dielectric constant, and the ionization constant pK_w use separate IAPWS formulations, subject to the limits below.

Supported pairs are P–T, P–h, P–s, h–s, T–h, T–s, P–x, and T–x. A two-phase calculation returns the mixture, both saturation endpoints, and the differences h_fg, s_fg, and v_fg.

Region numbers identify equation domains; phase labels describe the physical state. Detailed region boundaries are defined in IAPWS R7-97(2012).

Reference state: IAPWS sets the specific internal energy and entropy of saturated liquid to zero at the triple point (273.16 K, 611.657 Pa). Specific enthalpy follows h = u + pv, giving approximately 0.000611783 kJ/kg at that reference state. Use the same reference convention when comparing enthalpy and entropy across sources.

Saved calculations retain result snapshots and engine-version tags. Restore recalculates the saved inputs with the active engine and shows a notice if the displayed result differs from the saved result.

Verification coverage

The repository's CI workflow and configured Vercel deployment builds run these checks through npm run verify. A failed acceptance check stops that verification run before the application build. The limits describe agreement at the tested states; they are not uncertainty bounds for every state in the IF97 domain.

Forward and saturation checks use relative error. The P–h and P–s checks use absolute temperature differences of 0.010 or 0.025 K, as specified by each fixture. These checks exercise the public calculation path against the published backward check values; they do not report a measured worst-case error over the full domain.

NIST Chemistry WebBook supplies water reference data from a separate reference surface. The tests use a 0.1% limit for density, specific volume, internal energy, enthalpy, and entropy, and a separate 0.25% limit for c_p, c_v, and speed of sound at the ten benchmark states. These are project acceptance limits at the selected states.

The table lists the covered numerical benchmarks. Surface tension, static dielectric constant, and pK_w do not currently have official numerical check fixtures in this suite.

Primary sources

• IAPWS R7-97(2012), Revised Release on the Industrial Formulation 1997: equations, regions, and official verification tables.
• IAPWS R12-08, Viscosity of Ordinary Water Substance: Table 4 verification values.
• IAPWS R15-11, Thermal Conductivity of Ordinary Water Substance: base and industrial verification values.
• IAPWS R1-76(2014), Surface Tension of Ordinary Water Substance: liquid–vapor surface tension along the saturation curve.
• IAPWS R8-97, Static Dielectric Constant of Ordinary Water Substance: correlation and validity limits.
• IAPWS R11-24, Ionization Constant of H₂O: the 2024 temperature-and-density formulation used to calculate pK_w.
• NIST Chemistry WebBook SRD 69, Thermophysical Properties of Water: independent P–T spot checks.
• NIST SP 811, Appendix B.8: psi and Btu conversion factors.

Validity and limitations

Calculation limits

PhaseGauge supports 273.15–1073.15 K (0–800 °C) at pressures up to 100 MPa. Above 1073.15 K and up to 2273.15 K (2000 °C), the pressure limit is 50 MPa. All pressure limits here are absolute.

Single-phase pressure inputs start at 0.000611212677444 MPa, the IF97 saturation pressure at 273.15 K (0 °C). The P–x and T–x modes start at the triple point: 0.000611657 MPa and 273.16 K (0.01 °C). Saturation inputs must remain below the critical point: 22.064 MPa and 647.096 K (373.946 °C).

The pinned library applies mode-specific critical exclusions: P–T rejects the exact critical point T = 647.096 K and p = 22.064 MPa; T–h and T–s reject |T − 647.096 K| < 0.001 K at any pressure. Other inverse solves can reject critical endpoints or fail to converge. Nearby finite values remain available, including large heat capacities and isothermal compressibilities.

Ambiguous input pairs

On the liquid–vapor saturation boundary, P and T do not determine vapor quality. PhaseGauge rejects these P–T inputs; use P–x or T–x to specify saturated liquid (x = 0), saturated vapor (x = 1), or a mixture (0 < x < 1).

T–h and T–s can also match states at more than one pressure. The solver rejects ambiguous solutions. If pressure is known, use P–T away from saturation, P–h, or P–s; if quality is known, use P–x or T–x.

Near-critical states

PhaseGauge shows a near-critical advisory for states in the enlarged critical region defined in IAPWS R7-97(2012), Section 12, Figures 3–5: single-phase Region 3 states between the 0.0019 and 0.0069 m³/kg isochores and at or below 30 MPa. Saturation results receive the same advisory when either displayed endpoint lies in those bounds. IAPWS reports that heat-capacity and speed-of-sound uncertainties rise rapidly toward the critical point. This regional advisory supplies no numerical estimate of an individual result's error.

Supplemental properties

Supplemental properties have their own validity limits. The table describes availability in PhaseGauge within the calculator's pressure and temperature envelope. A dash (—) means that a value is unavailable or not reported for that state.

Viscosity uses the industrial form without the near-critical enhancement term. Thermal conductivity uses the industrial correlation with critical enhancement when the required state inputs are available. Surface tension is an interfacial property, not a bulk mixture average.

Generated table rows are direct equation evaluations. Equipment limits, boundary conditions, governing codes, and safety factors remain part of the engineering analysis that uses these properties.